Probability of Wave Behavior

Let's look at location prediction more closely. Using the Diffraction Suite program, choose Electrons. Set the slit separation to 15 nm and the kinetic energy to 20 eV.  Click Start.  You will get a pattern similar to the one shown here.

Now, suppose you were to send just one more electron through the slits. Where in the pattern that you just created is an electron is likely to strike? Make a prediction of the exact spot the next electron will strike.

To test your prediction, save your present pattern by dragging the screen to the right and start a new experiment. Move the Particles per Second slider to the left. Press the Start button. When just a few electrons hit the screen, press the Stop button.

How does the location of the dots match your earlier prediction?

In this experiment we restricted your predictions by limiting you to one location. Now, we will broaden your possibilities and have you make another prediction. This time we will add 100 electrons to the experiment.

Before you start make the following predictions:

• Examine your original pattern and describe the places where some electrons are very likely to be.
• Then describe locations where you are not sure if electrons will appear and places where you feel rather certain that there will be no electrons.

Now do the experiment and see how well you do. Click the Stop button when approximately 100 electrons have hit the screen.

As you see, we cannot state with certainty where the electrons will appear. However, we can discuss probabilities. The next electron has a very high probability of appearing in bright regions --- locations of constructive interference. Lower probabilities are associated with regions where the interference is between constructive and destructive. The probability of the electron appears at regions of destructive interference is essentially zero.

When learning quantum mechanics for the first time many students have difficulties with the wave function representation and the resulting probabilistic interpretation. Often the source of the students' difficulties is confusion about why we want to use a wave function to describe an electron as a wave function in the first place. In our experience an activity like this one at the beginning of a course provides the students with the evidence and the justification for moving from a deterministic to a probabilistic paradigm.